tnet: Software for Analysing Weighted Networks
tnet is a package written in R that can calculate weighted social network measures. Almost all of the ideas posted on this blog are related to weighted networks as, I believe, taking into consideration tie weights enables us to uncover and study interesting network properties. Not only are few social network measures applicable to weighted networks, but there is also a lack of software programmes that can analyse this type of networks. In fact, there are no open-source programmes. This hinders the use and development of weighted measures. tnet represents a first step towards creating such a programme. Through this platform, weighted network measures can easily be applied, and new measures easily implemented and distributed.
Continue Reading Add comment June 12, 2009
Weighted Rich-club Effect: A more appropriate null model for scientific collaboration networks
In this post, I extend the Weighted Rich-club paper
by suggesting and testing a different null model for the scientific collaboration network (Newman, 2001). This network is a two-mode network, which becomes an undirected one-mode network when projected. In the paper, we compared the observed weighted rich-club coefficient with the one found on random networks. The random networks were constructed by a null model defined for directed networks when prominence was based on node strength. Therefore, we created a directed network from the undirected scientific collaboration network by linking connected nodes with two directed ties that had the same weight. The null model consisted in reshuffling the tie weights attached to out-going ties for each node. However, this local reshuffling broke the weight symmetry of the two directed ties between connected nodes. The null model proposed in this post is based on the randomisation of the two-mode network before projecting it onto a one-mode network. By randomising before projecting, we are able to randomise a network while keeping the symmetry of weights. (Technical: 10/10)
Continue Reading Add comment May 29, 2009
Thesis: Structure and Evolution of Weighted Networks
I have now completed my Ph.D. at the School of Business and Management of Queen Mary College, University of London. My Ph.D. programme was defined around a number of projects, which drew on, and extended, recent theoretical and methodological advances in network science. The projects that were concerned with weighted networks and longitudinal networks were outlined and critically discussed in my thesis (Structure and Evolution of Weighted Networks). It is my hope and intention that the contributions made in the thesis have an impact on the community of researchers interested in networks. Although many parts have been published, the thesis contained a number of extensions. Therefore, in an effort to disseminate some of these, I have made most of the thesis available through this blog.
Continue Reading Add comment May 15, 2009
Projecting two-mode networks onto weighted one-mode networks
This post highlights a number of methods for projecting both binary and weighted two-mode networks (also known as affiliation or bipartite networks) onto weighted one-mode networks. Although I would prefer to analyse two-mode networks in their original form, few methods exist for that purpose. These networks can be transformed into one-mode networks by projecting them (i.e., selecting one set of nodes, and linking two nodes if they are connected to the same node of the other set). Traditionally, ties in the one-mode networks are without weights. By carefully considering multiple ways of projecting two-mode networks onto weighted one-mode networks, we can maintain some of the richness contained within the two-mode structure. This enables researchers to conduct a deeper analysis than if the two-mode structure was completely ignored. (Technical: 6/10)
Continue Reading Add comment May 1, 2009
Are triangles made up by strong ties?
A key assumption of Granovetter’s (1973) Strength of Weak Ties theory is that strong ties are embedded by being part of triangles, whereas weak ties are not embedded by being created towards disconnected nodes. This assumption have been tested by calculating the traditional clustering coefficient on binary networks created with increasing cut-off parameters (i.e., creating a series of binary networks from a weighted network where ties with a weight greater than a cut-off parameter is set to present and the rest removed). Contrarily to theories of strong ties and embeddedness, these methods generally showed that the clustering coefficient decreased as the cut-off parameter increased. However, the binary networks were not comparable with each other as they had a different number of ties. Another way of testing this assumption is to take the ratio between the weighted global clustering coefficient and the traditional coefficient measured on networks where all ties are considered present. Thus, the number of ties is maintained. This post highlights this feature and empirically tests it on a number of publically available weighted network datasets. (Technical: 5/10)
Continue Reading Add comment April 17, 2009
Article: Clustering in Weighted Networks
A paper called “Clustering in Weighted Networks” that I have co-authored will be published in Social Networks. Although many social network measures exist for binary networks and many theories differentiate between strong and weak ties, few measures have been generalised so that they can be applied to weighted networks and retain the information encoded in the weights of ties. One of these measures is the global clustering coefficient, which measures embeddedness or, more specifically, the likelihood of a triplet being closed by a tie so that it forms a triangle. This article proposes a generalisation of this key network measure to weighted networks.
Continue Reading Add comment April 3, 2009
The importance of allowing ties to decay
Recently, a number of network dataset have been constructed from archival data (e.g., email logs) with the aim to study human interaction. This has allowed researchers to study large-scale social networks. If the archival data does not included information about the severing or weakening of ties, non-relevant interaction among people, which occurred far in the past, might be deemed relevant. This post highlights this issue and suggests imposing a lifespan on interactions to record only relevant ties with the current strength. (Technical: 2/10)
Continue Reading Add comment March 20, 2009
Betweenness in weighted networks
This post highlights a generalisation of Freeman’s (1978) betweenness measure to weighted networks implicitly introduced by Brandes (2001) when he developed an algorithm for calculating betweenness faster. Betweenness is a measure of the extent to which a node funnels transactions among all the other nodes in the network. By funnelling the transactions, a node can broker. This could be by taking a cut (e.g. Ukraine controls most gas pipelines from Russia to Europe) or distorting the information being transmitted to its advantage. (Technical: 8/10)
Continue Reading Add comment February 20, 2009
Operationalisation of tie strength in social networks
The method used to operationalise ties’ strength into weights affects the outcomes of weighted networks measures. Simply assigning 1, 2, and 3 to three different levels of tie strength might not be appropriate as this scale might misrepresent the actually difference among the three levels (using an ordinal scale). In this post, I highlight issues with collecting weighted social network data from surveys. (Technical: 1/10)
Continue Reading 1 comment February 6, 2009
Weighted local clustering coefficient
The generalisation of the local clustering coefficient to weighted networks by Barrat et al. (2004) considers the value of a triplet to be the average of the weights attached to the two ties that make up the triplet. In this post, I suggest three additional methods for defining the triplet value. (Technical: 6/10)
Continue Reading 1 comment January 23, 2009
Average shortest distance in weighted networks
The average distance that separate nodes in a network became a famous measure following Milgram’s six-degrees of separation experiment in 1967 that found that people in the US were on average 6-steps from each other. This post proposes a generalisation of this measure to weighted networks by building on work by Dijkstra (1959) and Newman (2001). (Technical: 4/10)
Continue Reading 2 comments January 9, 2009
Local weighted rich-club measure
This post proposes a local (node-level) version of the Weighted Rich-club Effect (PRL 101, 168702). By incorporating this measure into a regression analysis, the impact of targeting efforts towards prominent nodes on performance can be studied. (Technical: 10/10)
Continue Reading 1 comment December 26, 2008
Network? Weighted network?
Networks are the cornerstone of this blog, therefore I have decided to make the first post my definition of a network and a few basic network measures. (Technical: 1/10)
Continue Reading Add comment November 28, 2008
